|Responsables :||Zoé Chatzidakis, Raf Cluckers.|
|Email des responsables :|
Pour recevoir le programme par e-mail, écrivez à : zchatzid_at_dma.ens.fr.
|Orateur(s)||Gal Binyamini - Weizmann Institute of Science,|
|Titre||Wilkie's conjecture for restricted elementary functions|
|Horaire||11:00 à 12:30|
|Résume||Let X be a set definable in some o-minimal structure. The Pila-Wilkie theorem (in its basic form) states that the number of rational points in the transcendental part of X grows sub-polynomially with the height of the points. The Wilkie conjecture stipulates that for sets definable in R_exp, one can sharpen this asymptotic to polylogarithmic.
I will describe a complex-analytic approach to the proof of the Pila-Wilkie theorem for subanalytic sets. I will then discuss how this approach leads to a proof of the “restricted Wilkie conjecture”, where we replace R_\exp by the structure generated by the restrictions of exp and sin to the unit interval (both parts are joint work with Dmitry Novikov). If time permits I will discuss possible generalizations and applications.